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Disc Covering Problem with Application to Digital Halftoning

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Abstract

This paper considers the following geometric optimization problem: Input is a matrix R=(r ij ). Each entry r ij represents a radius of a disc with its center at (i,j) in the plane. We want to choose discs in such a way that the total area covered by exactly one disc is maximized. This problem is closely related to digital halftoning, a technique to convert a continuous-tone image into a binary image for printing. An exact algorithm is given for the one-dimensional version of the problem while approximation algorithms are given for the two-dimensional one. The approximation algorithms are verified to be satisfactory in practice through experiments in applications to digital halftoning.

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Authors and Affiliations

  1. School of Information Science, JAIST, 1-1 Asahidai, Tatsunokuchi, Ishikawa, 923-1292, Japan

    Tetsuo Asano

  2. Department of Computer Science, City College, CUNY, Convent Avenue at 138th Street, New York, NY, 10031, USA

    Peter Brass

  3. Fuji Xerox Co., Ltd., 430 Sakai, Nakai, Ashigarakami, Kanagawa, 259-0157, Japan

    Shinji Sasahara

Authors
  1. Tetsuo Asano
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  2. Peter Brass
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  3. Shinji Sasahara
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Correspondence to Tetsuo Asano.

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Asano, T., Brass, P. & Sasahara, S. Disc Covering Problem with Application to Digital Halftoning. Theory Comput Syst 46, 157–173 (2010). https://doi.org/10.1007/s00224-008-9123-0

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  • DOI: https://doi.org/10.1007/s00224-008-9123-0

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